The ‘walkover’ before the Derby is a moment for owners to show off their horses and bask in the glory of 150,000 cheering fans

Like owners of sports teams, horse owners get their share of perks. And at the Kentucky Derby, there are few perks more coveted than the “walkover,” where beaming owners and their guests revel in the exclusive privilege of ruining a perfectly good pair of shoes.

The “walkover” is a short stroll with a simple purpose: Prior to Saturday’s race, which is slated to go off at about 6:44 p.m. ET, owners and trainers literally walk over...